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The Direct Numerical Simulation of turbulence is, conceptually at least, perhaps the simplest approach to the problem. Here, some arbitrary initial velocity field is set up and the Navier Stokes equations are used directly to describe the evolution of this field over time. It is then possible to carry out "measurements" on this field. The applications of DNS are diverse - it can be used to provide data for comparison with turbulence theories such as the Local Energy Transfer theory, it can be used to probe some of the more fundamental properties of turbulence as we are doing in our examination of renormalization group methods or it can be modified to simulate other phenomena, such as non-Newtonian effects. Though the idea seems straightforward, DNS requires considerable computational resources - our largest simulations take place on 256x256x256 grids which require 8 Gb of memory and we are hoping to tackle 512x512x512 grids soon which requires an enormous 32 Gb of memory. Given the size of the problem, we are fortunate to have access to the Cray T3D supercomputer, run by the Edinburgh Parallel Computing Centre. Here you can see some visualizations produced using the software package, AVS/Express.
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